Monday, July 15, 2013

1307.3280 (G. Berkolaiko et al.)

Combinatorial theory of the semiclassical evaluation of transport
moments II: Algorithmic approach for moment generating functions

G. Berkolaiko, J. Kuipers
Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, transport moments reduce to codifying classical correlations between scattering trajectories. These can be represented as ribbon graphs and we develop an algorithmic combinatorial method to generate all such graphs with a given genus. This provides an expansion of the linear transport moments for systems both with and without time reversal symmetry. The computational implementation is then able to progress several orders higher than previous semiclassical formulae as well as those derived from an asymptotic expansion of random matrix results. The patterns observed also suggest a general form for the higher orders.
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